Hospital (Trust) equipment Policies shall over-rule any "local" policies (the "cardio-resp" department in this case).
As mentioned on an earlier thread, kit like this should be given the "once over" (inspection for damage, at least) by a tech every time it appears on site ("walk-in clinic" or whatever). Also, both staff and patients must be encouraged (prevailed upon) to report faults. After all, the kit does not belong to them (neither the patients or the staff).
In my opinion, not having everything on the database (register) sounds like the slippery slope to negligence. What's it to be next ... what other equipment is to be disregarded in this way ... where do we draw the line?
As Dustcap mentions, all items of powered medical equipment should appear on the PM schedule, even if the inspection interval is "every five years" (I would max-out at one year, myself).
And yes, when (and wherever) "difficulties" are encountered, get those resisting to set down their objections in writing.
In passing, I have always advocated that all items belonging to each Hospital should be accounted for; biomed kit on the CMMS database, Estates stuff on whatever system they use (remember WIMS, anyone?) ... and all other property (chairs, et al) under Property Control.